SPIROGRAPH

As we all know through play, kids learn different things without even realizing it!

Playing with a spirograph, experimenting and trying all kinds of combinations, kids will develop mathematical and scientific intuition they can draw and realize the patterns, with the proper questions they can experiment, hypothesize, test, and generalize even reach conclusions.

Spirograph is a geometric drawing device that produces various mathematical curves known as hypotrochoids and epitrochoids.

The well-known toy version was developed by British engineer Denys Fisher and first sold in 1965. Original toy’s website: https://www.kahootztoys.com/spirograph-home.html

This image is taken from Smithsonian National Museum of American History

MATH:

The patterns that are created depend on three variables:

the radius of the fixed disc or wheel, (the number of teeth)
the radius of the revolving disc, (the number of teeth)
the location of the point on the moving disc.

By changing any one of these variables you can get tons of incredible and beautiful patterns.

Please check the Wolfram's collection of plane curves related with the curve names listed below.

A point on a wheel rolling inside a circle traces out a hypocycloid. A point on a wheel rolling on a flat surface traces out a curve called a cycloid. A point on a wheel rolling outside another wheel traces out an epicycloid.

A spirograph can be used to create artistically interesting patterns.

Besides the serious math behind it, the patterns can also be used to study;